Nonorientable manifolds with fundamental group of order
Authors:
Ian Hambleton, Matthias Kreck and Peter Teichner
Journal:
Trans. Amer. Math. Soc. 344 (1994), 649665
MSC:
Primary 57N13; Secondary 57Q20, 57R67
MathSciNet review:
1234481
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Abstract: In this paper we classify nonorientable topological closed 4manifolds with fundamental group up to homeomorphism. Our results give a complete list of such manifolds, and show how they can be distinguished by explicit invariants including characteristic numbers and the invariant associated to a normal structure by the spectral asymmetry of a certain Dirac operator. In contrast to the oriented case, there exist homotopy equivalent nonorientable topological 4manifolds which are stably homeomorphic (after connected sum with ) but not homeomorphic.
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 I. Hambleton and C. Riehm, Splitting of Hermitian forms over group rings, Invent. Math. 45 (1978), 1933. MR 0482788 (58:2840)
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 M. Ho Kim, S. Kojima, and F. Raymond, Homotopy invariants of nonorientable 4manifolds, Trans. Amer. Math. Soc. 333 (1992), 7181. MR 1028758 (92k:57033)
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 R. C. Kirby and L. R. Taylor, Pin structures on lowdimensional manifolds, Geometry of LowDimensional Manifolds. 2 (S. K. Donaldson and C. B. Thomas, eds.), London Math. Soc. Lecture Note Ser., vol 151, Cambridge Univ. Press, London and New York, 1989. MR 1171915 (94b:57031)
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 R. E. Stong, Notes on cobordism theory, Math. Notes, Princeton Univ. Press, Princeton, NJ, 1968.
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 C. T. C. Wall, Surgery on compact manifolds, London Math. Soc. Monographs 1, Academic Press, 1970. MR 0431216 (55:4217)
 [16]
 , Poincaré complexes. I, Ann. of Math. (2) 86 (1967), 231245.
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DOI:
http://dx.doi.org/10.1090/S00029947199412344812
PII:
S 00029947(1994)12344812
Article copyright:
© Copyright 1994 American Mathematical Society
